Materials modeling statistical correlations

A more common use of informatics for data analysis is the development of (quantitative) structure-property relationships (QSPR) for the prediction of materials properties and thus ultimately the design of polymers. Quantitative structure-property relationships are multivariate statistical correlations between the property of a polymer and a number of variables, which are either physical properties themselves or descriptors, which hold information about a polymer in a more abstract way. The simplest QSPR models are usually linear regression-type models but complex neural networks and numerous other machine-learning techniques have also been used. 

Another common theory was proposed by Manson (27) and is referred to as the universal slopes equation. In this model, the plastic strain or permanent deformation, is considered as a measure of the damage imposed in the material. On this basis, the true plastic strain amplitude can be used as a measure of the fatigue behavior. Moreover, the fatigue curve can be predicted in terms of the monotonic stress-strain curve. This empirical approach was initially statistically correlated with many metals and takes the following form ... 

In this study, the Nataf model (Ditlevsen Madsen 1996) was used to generate realizations of the random parameters 0. It requires specification of the marginal PDFs of the random parameters 0 and their correlation coefficients. It is therefore able to reproduce the given first- and second-order statistical moments of random parameters 0. The same three-dimensional three-story reinforced concrete building presented in Section 2.4, but on rigid supports, is considered as application example. Table 1 provides the marginal distributions and their statistical parameters for the material parameters modelled as correlated random variables. Other details on the modelling of the structure and the statistical correlation of the random parameters can be found in Barbato et al. (2006). 

Riccardo and coworkers [50, 51] reported the results of a statistical thermodynamic approach to study linear adsorbates on heterogeneous surfaces based on Eqns (3.33)—(3.35). In the first paper, they dealt with low dimensional systems (e.g., carbon nanotubes, pores of molecular dimensions, comers in steps found on flat surfaces). In the second paper, they presented an improved solution for multilayer adsorption they compared their results with the standard BET formalism and found that monolayer capacities could be up to 1.5 times larger than the one from the BET model. They argued that their model is simple and easy to apply in practice and leads to new values of surface area and adsorption heats. These advantages are a consequence of correctly assessing the configurational entropy of the adsorbed phase. Rzysko et al. [52] presented a theoretical description of adsorption in a templated porous material. Their method of solution uses expansions of size-dependent correlation functions into Fourier series. They tested... 

Once the model provides a good fit of experimental observations, the statistical certainties of the model parameters are inspected. If parameters are highly correlated, it is often possible to alter one parameter and compensate for the alteration with another parameter without compromising the fit of model. For example, in the compartmental model of the dynamics of )3-carotene metabolism, /3-carotene absorption was highly (positively) correlated with the irreversible loss of /3-carotene from the EHT compartment. Therefore, the absorption of /3-carotene and its irreversible loss from the EHT could be increased simultaneously, along with minor adjustments to a few other FTCs, without materially altering the compartmental model s prediction of the experimental observations. 

An attempt was made to find robust calibration equations for sugar content and acidity by MLR, PCR, and PLS, where the optical parameters were employed as explanatory variables. Normally, chemometrics by NIR spectra employs the absorbance as the explanatory variable, where only wavelength-dependent characteristics of the materials can be considered. In this case, it is very difficult to precisely evaluate the small amount of a constituent such as acid content in a fruit. On the other hand, chemometrics by TOF-NIRS would be related to both wavelength- and time-dependent characteristics as the explanatory variables, where the light absorption and light scattering phenomena in a sample are included. It may therefore be possible to detect the acid content in a fruit on the basis of this new optical concept. The statistical results are summarized in Tables 4.2.1 and 4.2.2. Figure 4.2.9 shows the PLS analysis in a optimum model for acidity in apple. In the case of normal analysis by second-derivative NIR spectra, standard error of calibration (SEC) and correlation coefficient between measured and predicted acidity r were limited to 0.048% and... 

The example structure is one quarter of a 1 in. thick, 32x32 in square composite plate with a 4-inch diameter circular core region under distributed edge loads, as shown in Fig. 5. The bulk and shear moduli K and G, respectively, of the outside material are modeled as homogeneous Gaussian random fields. The moduli and of the core material and the load intensity V/ are considered to be Gaussian random variables. The assumed means and coefficients of variation are listed in Table 2. The shear and bulk moduli for each material are assumed to be statistically independent, but correlation between the same moduli for the two materials, i.e, pG Gi is considered. 

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